The Lions started doing it in 1934 (their inaugural season) because they were trying to compete for space in the newspaper with the Detroit Tigers... and losing.

By playing on Thanksgiving, they guaranteed that they'd get the press.

The game ended up being a 'classic' and that set the tone for the tradition. They sold out the game weeks before (big news back then) and could have sold an estimated twice the available tickets. They've played on every T-Day since, except for between 1939-1945.

As for Dallas... who cares?

Again it was strictly for marketing purposes but I can't find any more 'specific' information than that they started in 1966.

It started with Detroit the first year they played. Lions vs the defending world champ Bears. 1934. It was really just way to get people in the seats, and people embraced it.
A Detroit Thanksgiving has had football forever. The only ones they missed were during World War II from '39-'44.